The present invention relates generally to receivers and more specifically to a receiver which compensates for the Doppler effect in the received signal.
Due to the computational complexity, the Global Positioning Satellite (GPS) receivers have been implemented in hardware, employing multiple parallel channels. Usually, each channel is responsible for tracking and demodulating one satellite. In some more sophisticated designs, for economic reasons, one channel can be time shared by more than one satellite. In the case of multi-protocol communication systems, the hardware implementation becomes less attractive due to extra chip cost and PC board area consumed.
Although the present receiver will be described in the context of a GPS receiver, the principles are applicable to any receiver which has a Doppler effect in the received signal resulting from the relative movement of the transmitter and the receiver.
The received GPS signal can be viewed as a superposition of Ns DS-CDMA signals coming from Ns visible satellites. Each satellite has its unique signature and slightly different carrier frequency due to the Doppler effect, even though they transmit at the same carrier frequency f. The composite GPS code signal can be modeled as (see Elliot D. Kaplan, Understanding GPS Principles and Applications, Artech House Inc. (1996)):
                                                                        s                ⁡                                  (                  t                  )                                            =                            ⁢                                                ∑                                      i                    =                    0                                                                              N                      s                                        -                    1                                                  ⁢                                                      ∑                                          n                      =                                              -                        ∞                                                                                    +                      ∞                                                        ⁢                                                            ∑                                              k                        =                                                  -                          ∞                                                                                            +                        ∞                                                              ⁢                                                                  A                        i                                            ⁢                                                                        d                          i                                                ⁡                                                  [                          k                          ]                                                                    ⁢                                              g                        ⁡                                                  (                                                      t                            -                                                          k                              ⁢                                                                                                                          ⁢                                                                                                N                                  p                                                                                                  f                                  i                                                                                                                                              )                                                                                                                                                                                                          ⁢                              g                ⁢                                  (                                      t                    -                                          n                      ⁢                                                                                          ⁢                                              1                                                  f                          i                                                                                                      )                                ⁢                                                                            P                      i                                        ⁡                                          [                                                                        (                                                      n                            +                                                          n                              i                              ′                                                                                )                                                ⁢                                                                                                  ⁢                        %                        ⁢                                                                                                  ⁢                                                  N                          p                                                                    ]                                                        ·                                      cos                    ⁡                                          (                                                                        2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            i                                                    ⁢                          t                                                +                                                  φ                          i                                                                    )                                                                                                                              (        1        )            wherein: Ai is the amplitude for satellite i, d[k] is the data in the kt millisecond, fi=1/Ti is the carrier frequency for the ith satellite, g(t−mTi)=σ(t−mTi) σ[(m+1)Ti−t)] is the window function,
      σ    ⁡          (      t      )        =      {                            1                                                    for              ⁢                                                          ⁢              t                        ≥            0                                                0                                                    for              ⁢                                                          ⁢              t                        <            0                              is the unit step function, Pi[n] the is the nth chip in the kth millisecond of the C/A code for satellite i, % means modulus operation, Np is the number of visible satellites and φi is the phase shift. In equation (1), the noise term has been deliberately ignored for commodity.
After multiplying the composite signal s(t) by a window function of the carrier frequency f=1/T and summing, equation (1) becomes:
                                                                        χ                ⁡                                  (                  t                  )                                            =                            ⁢                                                ∑                                      i                    =                    0                                                                              N                      s                                        -                    1                                                  ⁢                                                      A                    i                                    ⁢                                                            d                      i                                        ⁡                                          [                      k                      ]                                                        ⁢                                                                                    P                        i                                            ⁡                                              [                                                                              (                                                          n                              +                                                              n                                i                                ′                                                                                      )                                                    ⁢                                                                                                          ⁢                          %                          ⁢                                                                                                          ⁢                                                      N                            p                                                                          ]                                                              ·                                                                                                                                        ⁢                                                g                  ⁡                                      (                                          t                      -                                              n                        ⁢                                                                                                  ⁢                                                  1                                                      max                            ⁡                                                          (                                                              f                                ,                                                                  f                                  i                                                                                            )                                                                                                                                            )                                                  ·                                  cos                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          i                                                ⁢                        t                                            +                                              φ                        i                                                              )                                                  ·                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    f                    ⁢                                                                                  ⁢                    t                                                                                                          (        2        )            The integral of χ(t) over the entire time axis represents the Fourier transform of cos(2πfit+φi) times a constant:
                                                                                          ∫                                      -                    ∞                                                        +                    ∞                                                  ⁢                                                      χ                    ⁡                                          (                      t                      )                                                        ⁢                                      ⅆ                    t                                                              =                            ⁢                                                ∫                                      n                    ·                    T                                                                              (                                              n                        +                        1                                            )                                        ⁢                                                                                  ⁢                                          max                      ⁡                                              (                                                  T                          ,                                                      T                            i                                                                          )                                                                                            ⁢                                                      χ                    ⁡                                          (                      t                      )                                                        ⁢                                      ⅆ                    t                                                                                                                          =                            ⁢                                                ∫                                      n                    ·                    T                                                                              (                                              n                        +                        1                                            )                                        ·                                          max                      ⁡                                              (                                                  T                          ,                                                      T                            i                                                                          )                                                                                            ⁢                                                      ⅆ                    t                                    ⁢                                                                          ⁢                                                            ∑                                              i                        =                        0                                                                                              N                          s                                                -                        1                                                              ⁢                                                                  A                        i                                            ⁢                                                                        d                          i                                                ⁡                                                  [                          k                          ]                                                                    ⁢                                                                                                    P                            i                                                    ⁡                                                      [                                                                                          (                                                                  n                                  +                                                                      n                                    i                                    ′                                                                                                  )                                                            ⁢                                                                                                                          ⁢                              %                              ⁢                                                                                                                          ⁢                                                              N                                p                                                                                      ]                                                                          ·                                                                                                                                                                                  ⁢                                                cos                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          i                                                ⁢                        t                                            +                                              φ                        i                                                              )                                                  ·                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    f                    ⁢                                                                                  ⁢                    t                                                                                                                          =                            ⁢                                                ∫                                      n                    ·                    T                                                                              (                                              n                        +                        1                                            )                                        ·                                          max                      ⁡                                              (                                                  T                          ,                                                      T                            0                                                                          )                                                                                            ⁢                                                      ⅆ                    t                                    ⁢                                                                          ⁢                                      A                    0                                    ⁢                                                            d                      0                                        ⁡                                          [                      k                      ]                                                        ⁢                                                                                    P                        0                                            ⁡                                              [                                                                              (                                                          n                              +                                                              n                                0                                ′                                                                                      )                                                    ⁢                                                                                                          ⁢                          %                          ⁢                                                                                                          ⁢                                                      N                            p                                                                          ]                                                              ·                                                                                                                                        ⁢                                                                    cos                    ⁡                                          (                                                                        2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            0                                                    ⁢                          t                                                +                                                  φ                          0                                                                    )                                                        ·                                      ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      f                      ⁢                                                                                          ⁢                      t                                                                      +                                                                                                      ⁢                                                ∫                                      n                    ·                    T                                                                              (                                              n                        +                        1                                            )                                        ·                                          max                      ⁡                                              (                                                  T                          ,                                                      T                            1                                                                          )                                                                                            ⁢                                                      ⅆ                    t                                    ⁢                                                                          ⁢                                      A                    1                                    ⁢                                                            d                      1                                        ⁡                                          [                      k                      ]                                                        ⁢                                                                                    P                        1                                            ⁡                                              [                                                                              (                                                          n                              +                                                              n                                1                                ′                                                                                      )                                                    ⁢                                                                                                          ⁢                          %                          ⁢                                                                                                          ⁢                                                      N                            p                                                                          ]                                                              ·                                                                                                                                        ⁢                                                                    cos                    ⁡                                          (                                                                        2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            1                                                    ⁢                          t                                                +                                                  φ                          1                                                                    )                                                        ·                                      ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      f                      ⁢                                                                                          ⁢                      t                                                                      +                …                +                                                                                                      ⁢                                                ∫                                      n                    ·                    T                                                                              (                                              n                        +                        1                                            )                                        ·                                          max                      ⁡                                              (                                                  T                          ,                                                      T                                                                                          N                                s                                                            -                              1                                                                                                      )                                                                                            ⁢                                                      ⅆ                    t                                    ⁢                                                                          ⁢                                      A                                                                  N                        s                                            -                      1                                                        ⁢                                                            d                                                                        N                          s                                                -                        1                                                              ⁡                                          [                      k                      ]                                                                                                                                                            ⁢                                                                    P                                          N                                              s                        -                        1                                                                              ⁡                                      [                                                                  (                                                  n                          +                                                      n                                                                                          N                                s                                                            -                              1                                                        ′                                                                          )                                            ⁢                                                                                          ⁢                      %                      ⁢                                                                                          ⁢                                              N                        p                                                              ]                                                  ·                                                                                                      ⁢                                                cos                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                                                                                    N                              s                                                        -                            1                                                                          ⁢                        t                                            +                                              φ                                                                              N                            s                                                    -                          1                                                                                      )                                                  ·                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    f                    ⁢                                                                                  ⁢                    t                                                                                                          (        3        )            
In order to minimize the detection error for a particular satellite i resulting from the Doppler shift as well as for the phase shift, the following must be true f−fi=0 and φi=0 for each satellite. Conforming to the Fourier transform shifting property, the condition f−fi=0 can be achieved either through frequency or time domain shift.
In a hardware implementation, the carrier is tracked by advancing or retarding the local oscillator LO frequency and phase (frequency domain shift) conforming to the output of a Phase Locked Loop (PLL) circuit. The integrals in equation (3) are performed in parallel, each by a separate channel as shown in FIG. 1. The signal from the RF front end is digitized, demodulated and correlated against the satellite signature (PN number), and the results are transferred to the digital signal processor DSP for further processing. There is also a PLL block and local oscillator LO associated with each channel. Depending on cost/performance, a GPS receiver can incorporate from 4 to 12 channels.
The hardware architecture of the present receiver uses fewer hardware components and allows an efficient software implementation. It provides both flexibility and low power consumption.
The receiver includes an antenna for receiving a signal from a transmitter which is moving relative to the receiver. An A/D converter, connected to the antenna, provides a sampled digital signal from the input signal A controller receives and demodulates the sampled digital signal from the A/D converter. The controller shifts the sampled digital signal to compensate for Doppler effect in the input signal prior to demodulation. The controller compensates for a Doppler increased frequency by shifting the sampled digital signal so as to skip a sample period every n samples. This may be achieved by decreasing a cycle of m samples by one sample period every n samples. The controller compensates for a Doppler decreased frequency by shifting the sampled digital signal so as to add a sample period every n samples. This may be achieved by repeating a sample every n samples to shift the sampled digital signal.
The sampled digital signal is shifted until a known transmission frequency of the transmitter has been modified to match the frequency of the input signal. The controller matches the phase of the sampled digital signal to the phase of the input signal using, for example, a phase locked loop. The controller includes software for shifting and demodulating the sampled digital signal and the phase locked loop. The controller identifies how many transmitters' transmissions are in the input signal and demodulates and shifts the sampled data for each identified transmitter, in parallel.
These and other aspects of the present invention will become apparent from the following detailed description of the invention, when considered in conjunction with accompanying drawings.